Two forces parallel to the x-axis do 14.7 J of work on a small tray while moving it 20.7 m in the x direction across the gym floor. One of the forces has a value of +3.89 N in the x direction. What is the other force?
net force*distance=14.7
(f+3.89)*20.7=14.7
solve for f
To find the value of the other force, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. In this case, since the object moves only in the x-direction and the forces are also parallel to the x-axis, we can assume that the work done on the tray is entirely converted into its kinetic energy.
The work done by a force is given by the equation:
Work = Force × displacement × cos(θ)
where "Force" is the magnitude of the force, "displacement" is the magnitude of the displacement, and "θ" is the angle between the force and the displacement. In this case, the angle between the forces and the displacement is 0 degrees, so cos(θ) is equal to 1.
We are given that the total work done on the tray is 14.7 J, and one of the forces has a value of +3.89 N. We need to find the value of the other force, so let's call it "F".
Using the equation for work, we can set up the following equation:
14.7 J = (3.89 N + F) × 20.7 m × 1
Now, we can solve for "F":
14.7 J = (3.89 N + F) × 20.7 m
Divide both sides by 20.7 m:
F = (14.7 J / 20.7 m) - 3.89 N
Calculating the expression on the right side:
F = 0.710 N - 3.89 N
F = - 3.180 N
Therefore, the other force has a value of -3.180 N in the x direction.